Will reading books improve the enjoyment of anime?

Maybe if you read good books.

Varying your diet of fiction will generally improve your appreciation for other forms, improve your reading skills, improve your writing skills, and if you branch out into non-fiction, it will also simply make you a more learned human being.

It will also diminish the burnout associated with consuming a single type of medium, especially something relatively particular like anime.

Well lots of anime do not adapt the entire story and often they abridge the story to fit the run time. So if there's an anime that you really like, you may wish to check out the source LN or Manga to read the full story. In some case the anime adaptation is bad and the source is vastly superior. for example see the LN for So I'm a spider so what?

Potentially in certain areas. A lot of ways of more deeply appreciating anime like knowledge about cinematography, voice acting, animation, sound design, etc are not exactly found in novels, but training your attention span and your capacity for things like thematic analysis (if you train them on books) will transfer over.

As another comment said though, broadening your horizons and engaging with varied types of media generally is a good thing. When you come back, you'll have more colors to paint with.

eh, depends what type of learner you are. i prefer by doing. the more anime you watch, the more patterns, tropes, archetypes you pick up from the next anime. you could probably pick that up from books too, but if you are only doing it for the sake of enjoying anime, i wonder if that investment will pay off the way you want it to.

If you read good books, then yes. Stick to award winners, and you'll have a better grasp of narrative convention and storytelling tools.

If you just read random light novels before they are adapted to an anime, then no. The odds that they are either poorly written or poorly translated are high. And you won't learn anything from that.

If you want to read books sure do it. But reading won’t make anime more enjoyable necessarily

I think it would. Having a broad and varied media diet increases one's engagement with all other forms of media. Not only does it help improve attention span, critical thinking, imagination, vocabulary, etc., it also provides new perspectives and different methods of constructing prose, characters, and stories that anime may not tend towards as much which can help you analyze things in anime more wholistically. It also means you're familiar with other texts that anime might be engaging with, influenced by, or building from. Or if you read non-fiction you'll have more knowledge about subjects that anime might explore that will help you appreciate it more. Overall, I think it's only ever a good thing to experience many different kinds of media. Sticking only to anime or extremely adjacent media (like manga and light novels) is limiting. Experiencing many forms of art just makes you a more well rounded person.

At the very least, reading the light novels that an anime adapts will give you more details and better paced content in some instances (anime can't do everything right and has its own set of restrictions).

I heard that "Bookworm" is an amazing LN, the premise coincidentally is about someone who loves books.

Like all things, I think it greatly depends. Do you enjoy reading/did you enjoy reading in the past? If at some point, you were an avid reader, I think it definitely would positively impact your experience. I used to be read a lot of historical fiction, dystopian literature, and philosophy, and have been getting back to it recently. The more I read and watch, the more I realize how I'm starting to think more carefully about character decisions and the director/author's message. It's not just trying to understand it, but more of attempting to view it from different perspectives. To be honest, it also increased my attention span, which was something I was struggling with because I was finding it harder to get immersed in a show.

Even if you were not much of a reader before, I feel like it never hurts to test it out. It's a brain teaser, a test of your imagination, and a nice way to become engrossed in something new!

It'll improve your enjoyment and appreciation of good anime, but lessen your enjoyment of slop.  Especially if you read widely.  

Um... reading specifically? Probably not.

Engaging with other media will help with burnout and could help to give you better perspective on areas where anime excels and where there's maybe room for improvement, but that's not necessarily exclusive to reading.

If you want to better understand anime storytelling, then watch more anime. Books and film have different storytelling techniques that they use and training yourself on one is not gonna necessarily make your comprehension of the other better.

I guess? IDK, I go to reading, usually when I get burnt out on anime. There are some genres, that a lot of modern anime neglect, that you see more of in literary fiction. Also, it's just good to get away from YA writing sometimes.

IDK if reading improves my enjoyment of anime directly though. My enjoyment is improved, in that, I need to take a break every so often.

Absolutely!
I read Anne of Green Gables and it was ravishing, it greatly improved my vocabulary and the way I write

Somewhat tbh